As a last remark, we observe that frameworks over the complete graph, \((\mathcal {K}_N, p_{\mathcal {K}_N},R_{\mathcal {K}_N})\) , are (except for the degenerate configurations), infinitesimally rigid. That is, \(\textup {rank}(\widetilde{\mathcal {R}}_{\mathcal {K}_N}) =6N - 6\) . This result follows from the literature on distance- and \(\mathsf {SE}(3)\) -rigidity theory [1]}, [2]}. This leads to the following corollary.
